# Twisted and folded Auslander-Reiten quivers and applications to the representation theory of quantum affine algebras

@article{Oh2019TwistedAF,
title={Twisted and folded Auslander-Reiten quivers and applications to the representation theory of quantum affine algebras},
author={Se-jin Oh and Uhi Rinn Suh},
journal={Journal of Algebra},
year={2019}
}
• Published 1 October 2019
• Mathematics
• Journal of Algebra
12 Citations
This work is the sequel to Continuous Quivers of Type A (I). In this paper we define the Auslander-Reiten space of a continuous type $A$ quiver, which generalizes the Auslander-Reiten quiver of type
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For a complex finite-dimensional simple Lie algebra g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}
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Let $U_q'(\mathfrak{g})$ be a quantum affine algebra of arbitrary type and let $\mathcal{C}_{\mathfrak{g}}$ be Hernandez-Leclerc's category. We can associate the quantum affine Schur-Weyl duality
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Abstract In this paper, a new categorical crystal structure for the quantum affine algebras is presented. We introduce the notion of extended crystals B ^ 𝔤 ⁢ ( ∞ )
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Let $U_q'(\mathfrak{g})$ be a quantum affine algebra with an indeterminate $q$ and let $\mathscr{C}_\mathfrak{g}$ be the category of finite-dimensional integrable $U_q'(\mathfrak{g})$-modules. We
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We study deformations of cluster algebras with several quantum parameters, called toroidal cluster algebras, which naturally appear in the study of Grothendieck rings of representations of quantum
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Let $U_q'(\mathfrak{g})$ be a quantum affine algebra of untwisted affine ADE type and let $\mathcal{C}^0_{\mathfrak{g}}$ be Hernandez-Leclerc's category. For a duality datum $\mathcal{D}$ in
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Let $U_q'({\mathfrak {g}})$ be a quantum affine algebra with an indeterminate $q$, and let $\mathscr {C}_{\mathfrak {g}}$ be the category of finite-dimensional integrable $U_q'({\mathfrak • Mathematics Mathematische Zeitschrift • 2023 The ( q , t )-Cartan matrix specialized at $$t=1$$ t = 1 , usually called the quantum Cartan matrix , has deep connections with (i) the representation theory of its untwisted quantum affine algebra, ## References SHOWING 1-10 OF 38 REFERENCES • Se-jin Oh • Mathematics Mathematische Zeitschrift • 2018 We introduce new partial orders on the sequence positive roots and study the statistics of the poset by using Auslander–Reiten quivers for finite type ADE. Then we can prove that the statistics • Mathematics • 2016 We introduce and study the twisted adapted$r$-cluster point and its combinatorial Auslander-Reiten quivers, called twisted AR-quivers and folded AR-quivers, of type$A_{2n+1}$which are closely • Mathematics Communications in Mathematical Physics • 2019 We first compute the denominator formulas for quantum affine algebras of all exceptional types. Then we prove the isomorphisms among Grothendieck rings of categories$\${C_Q^{(t)} (t=1,2,3),
here, s, r are non-negative integers, and r ̂ s; also, given a polynomial/in the variable v and an integer a, we denote by fa the polynomial obtained from / by replacing v by v°9 for V 2s _ #~ s
Abstract We prove the Kirillov-Reshetikhin conjecture for all untwisted quantum affine algebras: we prove that the characters of Kirillov-Reshetikhin modules solve the Q-system and we give an
• Mathematics
• 1993
This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions
• Mathematics
• 2011
We obtain a presentation of the t-deformed Grothendieck ring of a quantum loop algebra of Dynkin type A, D, E. Specializing t at the the square root of the cardinality of a finite field F, we obtain
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• 2011
We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of Frenkel and Hernandez